Relay feedback methods combining sub-relays to reduce harmonics

The relay feedback method is considered to be one of the easiest identification methods available for obtaining the ultimate information of the process. It has been widely used in industry to automatically tune the PID controller. Many applications of the method have been developed. In this research, a new framework has been proposed to reduce the harmonics of the relay feedback signal. It linearly combined several sub-relay signals, which had different frequencies and gains and resulted in a significant reduction of harmonic terms. Improved versions of several previous relay feedback methods have been successfully developed on the basis of the proposed framework.